diff --git a/_chapters/survival-analysis-interactive/01-survival-data/01-diagram-1.png b/_chapters/survival-analysis-interactive/01-survival-data/01-diagram-1.png new file mode 100644 index 0000000..8c1758d Binary files /dev/null and b/_chapters/survival-analysis-interactive/01-survival-data/01-diagram-1.png differ diff --git a/_chapters/survival-analysis-interactive/01-survival-data/01-diagram-2.png b/_chapters/survival-analysis-interactive/01-survival-data/01-diagram-2.png new file mode 100644 index 0000000..a25173f Binary files /dev/null and b/_chapters/survival-analysis-interactive/01-survival-data/01-diagram-2.png differ diff --git a/_chapters/survival-analysis-interactive/01-survival-data/index.md b/_chapters/survival-analysis-interactive/01-survival-data/index.md new file mode 100644 index 0000000..57e78c6 --- /dev/null +++ b/_chapters/survival-analysis-interactive/01-survival-data/index.md @@ -0,0 +1,232 @@ +--- +title: 'Survival data and the survival curve' +--- + + + + +Survival analysis is a set of techniques used for modeling time to an event of interest. + +In survival analysis, the primary outcome we are interested in is the **time to an event of interest**. Each subject contributes two pieces of information: a **survival time** — a continuous value measured in days, months, or years — and an **event indicator** that records whether the event actually happened. The "survival" in survival analysis stems from its use in the study of the survival of patients. However, the event of interest can be many things: a disease relapse, the first technical failure of a car, or something as simple as the time until a newly acquired dental filling falls out. Many analysis methods would apply if the event occurred in all individuals. However, it is usual that at the end of a study, some individuals have yet to have the event of interest, and some might have ended their participation in the study beforehand for reasons other than experiencing the event. This doesn't mean that they won't necessarily experience the event in the future, but that their actual time to the event is unknown. This phenomenon is called **censoring**, and the data with an unknown true time to event is called **censored data**. Survival analysis includes a set of methods that can deal with datasets that include censored data. + +**Quick check.** + + answer.toLowerCase() === "true"} + options={["True", "False"]} + trials={2} + timeout={10}> + + + True. Survival analysis is exactly this family of methods: the outcome it models is the time until an event — a death, a relapse, or a filling falling out — occurs. + + + + + + + + Each subject contributes a continuous **survival time** (how long until the event or until we lose track of them) paired with a binary **event indicator** (1 if the event happened, 0 if the observation was censored). The other options miss this time-plus-event structure. + + + + + +Data with an unknown true time to event is called censored data. + +Let's look at the example from the videolecture. We gathered from a group of 10 friends when they last got a dental filling in the last ten years and when it fell out if it did. Can we estimate the probability of a new dental filling remaining in place after five years? + +Below we plotted the answers as a diagram. The x-axis marks the time from 2012 to 2022, and the lines represent when each person got their dental filling and how long it lasted. For instance, Bert got a dental filling in 2012, which lasted until 2015, and Fay got her's in 2014, which lasted until 2020. We have marked the friends whose dental filling fell out with a cross. However, two of the participants in this small study, Irene and Chloe, had their dental filling in place at the end of our observation window. And Harry and Fay did not lose their dental fillings, but for some reason or another, we do not know what happened to their dental fillings from 2020 to 2022. Perhaps they got them changed before the fillings had the chance to fall out. These four participants represent our censored data points. The time their dental fillings stayed in place still tells us something about how long fillings usually last. So instead of discarding their data, we mark them with a circle. + +![](01-diagram-1.png) + +This data represents an example of right censoring, but we also know cases with left- and interval censoring. Left-censoring would mean that we observe the presence of a state or condition but do not know when it began. Interval censoring, on the other hand, means that individuals come in and out of observation. This tutorial focuses only on right-censoring since this is how most survival data is censored. + +**Quick check.** + + answer.toLowerCase() === "true"} + options={["False", "True"]} + trials={2} + timeout={10}> + + + True. If the event hasn't occurred by the end of observation, we don't know the true event time — only that it is longer than the time we observed. That is right-censoring. + + + + +A minimal survival dataset is thus composed of observations with a survival time and event variable. The latter specifies if the event has, in fact, occurred (event=1) or whether it has been censored (event=0). We can transform our dental fillings data plotted as a diagram into a data table suitable for survival analysis. Since we are interested in how much time the dental filling lasted and not exactly what year it fell out, we re-plot the diagram, aligning when each person got their cavity filled to time 0. + +![](01-diagram-2.png) + +We can now easily transform this diagram into a data table. We order the data instances by time so that Anthony - whose time to his filling falling out is the shortest - is first, Bert is second, followed by Chloe, and so on. The third column contains the data on event censoring. On the diagram, we've marked Anthony and Bert with a cross, which means their filling fell out. Under their names in the table, we input a 1. But Chloe is marked with a circle since her filling has yet to fall out by the end of 2022, so we input a 0. We do the same for others. We have successfully prepared the data for the application of survival analysis methods. + +**Quick check.** + + answer.toLowerCase() === "true"} + options={["True", "False"]} + trials={2} + timeout={10}> + + + True. The event indicator is binary: 1 means the event was observed (the filling fell out), 0 means the observation was censored. + + + + + + + + +The survival function gives the probability of surviving past a particular time. + +We now have the data nicely organized. Back to our original question: *how likely is a new dental filling to stay in place after five years?* + +Intuitively, the probability of this happening **increases over time** because minor damages to and around the dental filling accumulate as time goes by. These damages can be due to the *type of filling and its interaction with the bacterial biofilm, your diet, saliva composition, mechanical forces*, etc. However, when we visually represent such data, we want to plot the probability of **the event not happening**. In this case, the probability of the dental filling *not falling out*. To put it a bit crudely, we are interested in the probability of it **surviving in your mouth as time passes**. + +We can estimate the **survival function** - *the probability of surviving past a particular time* - using the **Kaplan-Meier estimator**. Let's calculate the survival probability and its changes over time *by hand*. + +## Computing the curve, step by step + +On the x-axis, we mark the time in years, and on the y-axis, the probability of the dental filling staying in place. Assuming the dentist did a good job, the probability of the filling being in place at time zero is exactly 1. Everyone walks out of the clinic with their filling intact. + + + +- **Years 0–2.** No one loses their filling in the first two years. The probability stays at 1. +- **Year 2.** Anthony's filling falls out. One out of ten people who were *at risk* loses their filling, so the survival probability drops by a factor of 1/10. The new probability is 0.9. +- **Years 2–3.** Nothing else changes. The curve stays flat at 0.9. +- **Year 3.** Bert's filling falls out, and Chloe is censored. At this point Anthony has already failed, so nine people are at risk. The probability of staying in place *given that you made it to year 3* is 1 − 1/9 ≈ 0.89. Survival is cumulative, so we multiply by the previous value: 0.89 × 0.9 ≈ 0.8. +- **Years 3–4.** Flat again at about 0.8. +- **Year 4.** David and Elle both lose their fillings. How many were at risk going into year 4? We started with 10. Anthony failed at year 2; Bert failed at year 3; and Chloe — although she did *not* fail — was censored at year 3, so she leaves the at-risk pool too. That leaves seven people at risk. Two of them fail, so the local survival probability is 1 − 2/7. Multiply by the running value: (1 − 2/7) × 0.8 ≈ 0.57. + +Notice what happened with Chloe. She did not fail, but the fact that she was *censored* — that we lost track of her — removed her from the denominator. That is how Kaplan–Meier folds censored observations into the calculation without either discarding them or counting them as failures. + + + + + + If the study ends before the filling falls out, we do not observe the event in that study window. Gabe still contributes follow-up time up to the cutoff, but his event indicator would be 0. + + + + + + + + Shortening the study means we stop watching earlier. Events that happen after the cutoff are not observed as events in that dataset. Those subjects still contribute information up to the cutoff, but their event indicator is 0. + + + + + + + +The Kaplan–Meier plot is a visual representation of the survival function. + +We make these small calculations for the rest of the time points and draw the steps until we reach the end of our 10-year observation window. The graph we have produced is the Kaplan-Meier plot, which is one of the most used plots in survival analysis. It shows us how the survival probability changes over time. + +**Quick check.** + + answer.toLowerCase() === "false"} + options={["True", "False"]} + trials={2} + timeout={10}> + + + False. The curve plots the probability of *surviving past* a given time — the probability that the event has *not* happened yet. It starts at 1 and steps downward as events occur. + + + + + +The survival median is the time at which the survival probability drops to 0.5. + +So, for instance, if we want to know the time at which the survival probability drops to 0.5, we can read it on the plot. Look for the point where the curve has fallen to 50% and note the corresponding time on the x-axis. In the literature, this time, called the survival median, is often marked on the Kaplan-Meier plot. + +Doing the calculation by hand once builds intuition. After that, we let a computer do the arithmetic. Below is the same ten-friends dental fillings dataset loaded into the **Kaplan–Meier** widget. The curve should be identical to the one we worked out in the previous steps. Interact with the widget to confirm if the curve and calculated statistics match what you got by hand. + +**Try this - interact with the widget to confirm if the curve and calculated statistics match what you got by hand.** + + + + + + + + + The median survival time is the point where the survival probability drops to 0.5. Reading off the curve, that happens at seven years — half of the fillings are expected to have fallen out by then. + + + + + +## Takeaway + +Survival data is special because it is almost always incomplete: at the end of any study, some individuals have not yet had the event. **Censoring** is the name for that partial information, and it is information — not missing data. The **Kaplan–Meier estimator** uses both events and censored observations to estimate the probability of surviving past each point in time. + +The story works just as well when "friends and fillings" becomes "patients and tumors," which is where the next module picks up. diff --git a/_chapters/survival-analysis-interactive/01-survival-data/survival_curve.svg b/_chapters/survival-analysis-interactive/01-survival-data/survival_curve.svg new file mode 100644 index 0000000..5b63cc3 --- /dev/null +++ b/_chapters/survival-analysis-interactive/01-survival-data/survival_curve.svg @@ -0,0 +1,102 @@ + + + + + + + + + + + 1 + 0.9 + 0.8 + 0.7 + 0.6 + 0.5 + 0.4 + 0.3 + 0.2 + + + 0 + 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + + + SURVIVAL PROBABILITY + DURATION [YEARS] + + + + + + + + + + + + + + + + + + + + + + + + + + 9/10×1=0.9 + + + + 8/9×0.9=0.8 + + + + 5/7×0.8=0.57 + + + + . . . + + + diff --git a/_chapters/survival-analysis-interactive/01-survival-data/survival_curve_old.svg b/_chapters/survival-analysis-interactive/01-survival-data/survival_curve_old.svg new file mode 100644 index 0000000..73de161 --- /dev/null +++ b/_chapters/survival-analysis-interactive/01-survival-data/survival_curve_old.svg @@ -0,0 +1,114 @@ + + + + + + + + + + + 1 + 0.9 + 0.8 + 0.7 + 0.6 + 0.5 + 0.4 + 0.3 + 0.2 + + + 0 + 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + + + SURVIVAL PROBABILITY + DURATION [YEARS] + + + + + + + + + + + + + + + + + + + + + + + + + + 9/10×1=0.9 + + + + 8/9×0.9=0.8 + + + + 5/7×0.8=0.57 + + + + . . . + + + + + + + + 50% + MEDIAN SURVIVAL + + + diff --git a/_chapters/survival-analysis-interactive/01-survival-data/widget-placeholder.svg b/_chapters/survival-analysis-interactive/01-survival-data/widget-placeholder.svg new file mode 100644 index 0000000..2871389 --- /dev/null +++ b/_chapters/survival-analysis-interactive/01-survival-data/widget-placeholder.svg @@ -0,0 +1,7 @@ + + + + Interactive widget + iframe will be embedded here + + diff --git a/_chapters/survival-analysis-interactive/02-forming-and-comparing-groups/index.md b/_chapters/survival-analysis-interactive/02-forming-and-comparing-groups/index.md new file mode 100644 index 0000000..65d73d6 --- /dev/null +++ b/_chapters/survival-analysis-interactive/02-forming-and-comparing-groups/index.md @@ -0,0 +1,122 @@ +--- +title: 'Forming and Comparing Groups' +--- + +**Besides the survival time and event information, observations in a survival dataset are often characterized with a feature or two. We can use the features to form groups and compare their survival curves. Forming groups differs whether the feature is categorical or continuous.** + +Returning to our previous example, we have expanded the dental fillings dataset to include 10 more samples and three additional features. + +The first additional feature concerns the type of material out of which the dental filling was made of. It turns out they were either composite or ceramic, so type of material is a categorical feature. Anthony got a composite filling, and so did Bert, however, Chloe got a ceramic one and so on. The second additional feature is named Brushing time and denotes the average amount of time in minutes someone spends brushing their teeth daily. Anthony uses an electric toothbrush, so he's timed his brushing to 4 minutes daily, while Bert says he takes a bit more time. Chloe, on the other hand, has braces and thus spends 15 minutes per day brushing her teeth. Brushing time is a numeric feature, meaning its values are continuous. Lastly, there is another categorical feature, this one denoting whether the subject of the study prefers cats or dogs. + +**See the table below:** + + + + +To form groups based on a categorical feature, we split participants based on the category to which they belong. + +When we have a categorical feature, such as the type of material, it's easy to form groups of data instances. In our case, one group were friends with ceramic filling, and the other friends with composite filling. We can draw two survival curves on the same plot, each one corresponding to the filling type. + + + + + + + + + + + The survival curve for the ceramic group stays higher than the composite curve over the observed time. Ceramic dental fillings have a better prognosis of staying in place than composite ones. + + + + + + + + Hint: Check the legend and look for the composite group row. + + The legend reports the number of non-censored observations out of all the participants within a group (e.g., 8/10 for the group with the composite filling) and the median survival time for each group (5 years for the group with the composite filling). + + + + + +To form groups based on a continuous feature, we have to define a threshold and split participants based on that threshold. + +On the other hand, if we want to group by a continuous feature we have to define a threshold value to form groups. We will form two groups, one whose members brush their teeth more than six minutes a day, and the other one whose members brush less than that. + +### **Try this:** + +Below, set the threshold to **brushing time > 6 minutes**. Then use the Kaplan-Meier widget and group by the newly created feature (called 'Selected'). Two curves should appear — one for those that brush more than 6 minutes a day, one for those that brush less. Feel free to experiment with different thresholds and see how the curves change. + + + + + + + + + + + Grouping the subjects of our study by material type made a more considerable difference in the survival curve than grouping by brushing time. We gathered this just by visually inspecting the data. + + + + +Of course, it doesn't make sense to use just any feature to form groups. Not all features affect survival, so not all of them will separate the data into groups with different survival curves. For instance, one can assume that whether a person prefers dogs to cats does not affect how long their dental filling lasts. We can check this by forming groups by the last feature which contains information on whether the person prefers cats or dogs. The survival curves are barely separated. Preferring dogs to cats really doesn't affect the survival of dental fillings. + +Switch the grouping variable to **cats or dogs**. + + + + + The survival curves are barely separated. Preferring dogs to cats really doesn't affect the survival of dental fillings — not every feature in a dataset will separate the data into groups with different survival outcomes. + + + + + +To evaluate the difference between survival curves we use the log-rank test. + +Although visual inspection is a useful way of exploring the data, there is of course a more systematic way of comparing how well a particular feature separates the survival curves which is called the [**log-rank test**](https://www.wikiwand.com/en/Logrank_test). It computes how likely the difference between survival curves is not random. The smaller the p-value, the more likely our feature actually separates the data into groups with different survival outcomes. We can see this value next to the Kaplan-Meier plot. Grouping by type of material gives us a smaller p-value. diff --git a/_chapters/survival-analysis-interactive/02-forming-and-comparing-groups/select-rows-placeholder.svg b/_chapters/survival-analysis-interactive/02-forming-and-comparing-groups/select-rows-placeholder.svg new file mode 100644 index 0000000..08f73f9 --- /dev/null +++ b/_chapters/survival-analysis-interactive/02-forming-and-comparing-groups/select-rows-placeholder.svg @@ -0,0 +1,7 @@ + + + + Select Rows widget + iframe will be embedded here + + diff --git a/_chapters/survival-analysis-interactive/02-forming-and-comparing-groups/widget-placeholder.svg b/_chapters/survival-analysis-interactive/02-forming-and-comparing-groups/widget-placeholder.svg new file mode 100644 index 0000000..2871389 --- /dev/null +++ b/_chapters/survival-analysis-interactive/02-forming-and-comparing-groups/widget-placeholder.svg @@ -0,0 +1,7 @@ + + + + Interactive widget + iframe will be embedded here + + diff --git a/_chapters/survival-analysis-interactive/03-exploring-clinical-features/index.md b/_chapters/survival-analysis-interactive/03-exploring-clinical-features/index.md new file mode 100644 index 0000000..61214de --- /dev/null +++ b/_chapters/survival-analysis-interactive/03-exploring-clinical-features/index.md @@ -0,0 +1,112 @@ +--- +title: 'Exploring Clinical Features' +--- + +We previously estimated the difference in survival between two cohorts on a Kaplan-Meier plot and manually identified the feature that led to cohorts with distinct survival characteristics. However, real world survival datasets often include more than just 3 features to choose from. This time we will be working with a larger, clinical dataset, and we will start by exploring its features manually — one at a time, exactly as we did with the dental fillings. + +For this example let's use the **German Breast Cancer Study Group** data. The first two columns show the time and event. Specifically the Recurrence Free Survival Time, the time between the start of the study and the recurrence of cancer. The rest of the data is full of other clinical variables. Some of them categorical, like tumor grade, and other continuous ones, like the patient's age. + + + + +We already know how to form and compare groups manually. For categorical features, we simply select the feature in the Kaplan-Meier widget. There are three categorical features to choose from: Tumor Grade, Menopausal Status, and Hormonal Therapy. + + + + + +### **Try this:** + +Group by **Menopausal Status**. Then switch to **Hormonal Therapy**. Optionally, plot the median survival time and the confidence intervals to get a better idea of the data. + + + + + Being in menopause doesn't really have much effect on recurrence-free survival; the curves are barely separated, and the p-value is quite large. + + + + + + + + The patients that did not receive hormonal therapy had a significantly worse prognosis. The p-value should be much smaller than for Menopausal Status. + + + + +Using numeric features to form cohorts takes an extra step; we need to define a threshold to split the data. Say we're interested in whether there is a significant difference in survival between patients above and below the age of 60. The widget below lets you pick a numeric feature and slide the threshold. + + + + + + + + + + +### **Try this:** + +Set the feature to **Age** and the threshold to **60**. Then lower the threshold to **40**. + + + + + Whether a patient is above or below 60 doesn't make a big difference in the survival probability over the observed time. With the threshold at 40, there is a more significant difference between the survival curves. + + + + +Switch the feature to **Progesterone receptor** and put the threshold in the lowest bin — it already contains more than half the patients. + + + + + This time we really see a big difference between the two survival curves. Progesterone receptor level is informative for recurrence-free survival in this cohort. + + + diff --git a/_chapters/survival-analysis-interactive/03-exploring-clinical-features/widget-placeholder.svg b/_chapters/survival-analysis-interactive/03-exploring-clinical-features/widget-placeholder.svg new file mode 100644 index 0000000..2871389 --- /dev/null +++ b/_chapters/survival-analysis-interactive/03-exploring-clinical-features/widget-placeholder.svg @@ -0,0 +1,7 @@ + + + + Interactive widget + iframe will be embedded here + + diff --git a/_chapters/survival-analysis-interactive/04-ranking-survival-features/index.md b/_chapters/survival-analysis-interactive/04-ranking-survival-features/index.md new file mode 100644 index 0000000..5485ec6 --- /dev/null +++ b/_chapters/survival-analysis-interactive/04-ranking-survival-features/index.md @@ -0,0 +1,78 @@ +--- +title: 'Ranking Survival Features' +--- + +Up until now we have been forming and comparing groups by hand — one feature at a time, picking thresholds ourselves. That works when there is only a handful of clinical variables to consider, but real survival datasets often include dozens, and molecular datasets reach into the thousands. To explore at that scale we need a more systematic way of asking the same question — *does this feature separate survival?* — for every feature at once. + + +The Rank Survival Features widget uses the median value as a threshold for the continuous features. + + +Let's look at the **Rank Survival Features** widget, which forms cohorts by splitting samples at the median value for continuous features (and by category for categorical features), then evaluates the difference in survival between those cohorts using the log-rank test. There's a selection of two scoring methods for establishing which feature is most predictive of survival; we'll stick with the multivariate log-rank test. + + + +
+
+ +
+ +
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+ + +### **Try this:** + +Sort the features by p-value, then click on the top-ranked one. The Kaplan-Meier curve appears below — patients split at the median, with the above-median group in red. Then click through the other features in order of p-value and compare the gaps. + + + + + Sorted by p-value, the most informative feature is the Number of Positive Nodes. Positive nodes refer to lymph nodes in the armpit area where metastatic cancer cells have been found — one of the oldest and strongest prognostic markers in breast cancer. + + + + + + + + The red curve (patients with above-median positive node counts) drops much faster than the curve for patients at or below the median. More involved lymph nodes mean more advanced metastatic spread, which translates to a shorter time to recurrence — a worse prognosis. + + + + + + + + A small p-value tells you the difference is unlikely to be chance. It does *not* by itself tell you that the feature is biologically important, causal, or large in effect size. Keep these separate in your head. + + + + +We successfully identified the most informative feature regarding survival just with a few clicks. diff --git a/_chapters/survival-analysis-interactive/04-ranking-survival-features/widget-placeholder.svg b/_chapters/survival-analysis-interactive/04-ranking-survival-features/widget-placeholder.svg new file mode 100644 index 0000000..2871389 --- /dev/null +++ b/_chapters/survival-analysis-interactive/04-ranking-survival-features/widget-placeholder.svg @@ -0,0 +1,7 @@ + + + + Interactive widget + iframe will be embedded here + + diff --git a/_chapters/survival-analysis-interactive/05-advanced-topics/index.md b/_chapters/survival-analysis-interactive/05-advanced-topics/index.md new file mode 100644 index 0000000..c7fda2f --- /dev/null +++ b/_chapters/survival-analysis-interactive/05-advanced-topics/index.md @@ -0,0 +1,13 @@ +--- +title: 'Beyond Survival Curves' +omitAsChapter: true +--- + +A few directions worth knowing about: + +- **Cox proportional hazards regression.** Kaplan–Meier compares groups one feature at a time. The Cox model lets you fit several features together and estimate the effect of each *while holding the others fixed* — for example, the effect of tumor grade after adjusting for stage. This is the standard tool for adjusted survival analysis in biomedicine. +- **Confounding and multivariate adjustment.** As noted at the end of the previous module, simple two-group comparisons can mislead. As Clark et al. (2003) and Bradburn et al. (2003) put it: if one treatment group happens to be younger than the other, a naïve Kaplan–Meier might attribute better outcomes to the treatment when really age is doing the work. Multivariate models — Cox regression and its many extensions — exist to handle exactly this. +- **Beyond the proportional hazards assumption.** The Cox model assumes that the relative effect of a feature is constant over time. When it is not — for example, when a treatment helps in the short term but not the long term — there are more flexible alternatives (time-varying coefficients, parametric survival models, accelerated failure time models, random survival forests). +- **From clinical features to molecular biology.** We worked exclusively with clinical variables here. A natural next step is to bring in molecular data — gene expression, mutations, or summarized pathway activity scores — and ask which biological pathways influence survival, alone or after adjusting for clinical factors. + +Survival analysis is one of those rare areas of statistics where the simple tools (Kaplan–Meier, log-rank) carry you a remarkably long way *and* the more advanced tools sit on the same intuitions. If the staircase-shaped curve makes sense to you, you have a solid foundation for everything else. diff --git a/survival-analysis-interactive/01-time-to-an-event/index.md b/survival-analysis-interactive/01-time-to-an-event/index.md new file mode 100644 index 0000000..b0e7ac2 --- /dev/null +++ b/survival-analysis-interactive/01-time-to-an-event/index.md @@ -0,0 +1,25 @@ +--- +title: 'The Data and Survival Curve' +subTitle: 'A gentle introduction to survival analysis.' +chapters: + - survival-analysis-interactive/01-survival-data +--- + +**What is special about survival data? What is censoring? How do we visually represent changes in survival probabilities over time? In these chapters, we will go through some basic concepts of survival analysis. We will work with a toy example of survival data and show how to plot the survival curve, one of the key visualizations in survival analysis.** + + +Understanding how long something lasts before an event occurs—be it a machine breaking down, a product failing, or a dental filling falling out—is at the heart of survival analysis. Unlike standard statistical methods that expect a complete outcome for every case, survival analysis is uniquely suited to handle incomplete information through the concept of censoring. Here we will introduce survival data, explain how to prepare it for analysis, and demonstrate how to visualize time-to-event outcomes using the survival curve. Through a relatable example involving dental fillings, we’ll explore how to handle censored observations and estimate survival probabilities with tools like the Kaplan-Meier estimator—both manually and using the Orange data mining platform. Following are main concepts that we will cover: + +- **Survival Analysis**: A way to study how long it takes for something to happen. + +- **Event**: The outcome we are observing, like a dental filling falling out. + +- **Censoring**: When the event hasn’t (yet) happened during the study or its timing is unknown. + +- **Survival Time**: The time from the beginning of observation until the event or censoring. + +- **Kaplan-Meier Curve**: A graph showing the chance of the event not happening over time. + +**Start by watching the following video or if you prefer, you can skip it and start reading the lecture notes below.** + + diff --git a/survival-analysis-interactive/02-exploring-survival-features/index.md b/survival-analysis-interactive/02-exploring-survival-features/index.md new file mode 100644 index 0000000..ed4c19a --- /dev/null +++ b/survival-analysis-interactive/02-exploring-survival-features/index.md @@ -0,0 +1,37 @@ +--- +title: 'Exploring Survival Features' +subTitle: 'Forming and comparing groups.' +chapters: + - survival-analysis-interactive/02-forming-and-comparing-groups + - survival-analysis-interactive/03-exploring-clinical-features + - survival-analysis-interactive/04-ranking-survival-features +--- + +**In this chapter, you will learn how to create groups of samples (subjects, patients) using additional features from the data set and how to assess whether these groups showcase a difference in survival. You will also learn how to automatically rank and find the data features that best correlate with survival.** + +In survival analysis, we are often interested not just in how long something lasts, but in *why* it lasts longer in some cases than others. By exploring additional features in our dataset—like material type or brushing habits—we can form meaningful groups and compare their survival outcomes. This helps us uncover which factors might influence longevity. In this chapter, we will learn how to group data, compare survival curves, and identify the most informative features. We will cover the following concepts: + +- **Categorical Feature**: A variable with distinct categories, like material type (ceramic or composite), used to form groups for comparing survival. + +- **Continuous Feature**: A variable with a range of numeric values, like brushing time, requiring thresholds to split into groups. + +- **Data Grouping**: The process of dividing data based on a feature to compare survival curves between subgroups. + +- **Kaplan-Meier Curve**: A graph showing survival over time, used here to compare different groups based on selected features. + +- **Log-Rank Test**: A statistical test that checks whether the difference between two survival curves is likely due to chance. + +- **Threshold**: A chosen value used to split a continuous feature into two groups (e.g., brushing more or less than 6 minutes). + +- **Feature Ranking**: Automatically evaluating which features best separate the data into groups with different survival outcomes. + +- **P-Value**: A number indicating whether the difference in survival between groups is statistically significant (typically below 0.05). + +- **Discretization**: Converting a continuous feature into categorical bins to enable group comparisons. + + +**Start by watching the following videos or if you prefer, you can skip them and start reading the lecture notes below.** + + + + diff --git a/survival-analysis-interactive/04-where-to-go-from-here/index.md b/survival-analysis-interactive/04-where-to-go-from-here/index.md new file mode 100644 index 0000000..aff1a15 --- /dev/null +++ b/survival-analysis-interactive/04-where-to-go-from-here/index.md @@ -0,0 +1,8 @@ +--- +title: 'Where to go from here' +subTitle: 'Extending survival analysis beyond Kaplan–Meier.' +chapters: + - survival-analysis-interactive/05-advanced-topics +--- + +If you have worked through the two previous modules, you have met the core of survival analysis: events and censoring, the Kaplan–Meier curve, grouping by categorical and continuous features, the log-rank test, and ranking clinical features by how cleanly they separate survival. That is enough to read a great deal of the clinical and biomedical literature, and enough to ask sharper questions about your own data. But it is the *beginning*, not the end. diff --git a/survival-analysis-interactive/collection.md b/survival-analysis-interactive/collection.md new file mode 100644 index 0000000..0e57ae2 --- /dev/null +++ b/survival-analysis-interactive/collection.md @@ -0,0 +1,16 @@ +--- +title: Tutorial on Survival Analysis +subTitle: A short introduction to survival analysis. +coverImg: owkaplanmeier.svg +--- + +How long until something happens — a tooth filling fails, a tumor recurs, a patient relapses? Survival analysis is the toolbox for answering that question when not every story has ended yet. This is a short, hands-on introduction designed for biomedical researchers with little or no background in survival analysis or computational data analysis. + +You will not need to install anything. Every widget in this tutorial is embedded directly on the page, pre-loaded with data and ready for you to interact with. There are two short modules: + +1. **Time to an event** — what survival data looks like, why it is special, and how to draw a survival curve. +2. **What makes patients differ?** — using clinical features to split a breast cancer cohort and ask which factors matter for outcome. + +Throughout, look for the **Try this** prompts next to each widget. They will guide you through the interactive exercises, and you can check your understanding with the questions that follow. + +This material is offered under the Creative Commons [CC BY-NC-ND licence](https://creativecommons.org/licenses/by-nc-nd/4.0/).